Invisalign is a tool for developing a beautiful smile like any other. It is good for certain tooth movements, but is less efficient for other movements. Every patient's treatment needs to be individualized to their goals and their face. Sometimes Invisalign is a good idea and sometimes it is not, but I wouldn't use the word "can't" for tooth movements than can be achieved.
Through time consuming review of your ClnCheck by your orthodontist, proper staging and force application can be prescribed into your computerized tooth movements to move teeth vertically within reason. Additionally, with the use of TADs significant intrusion (another type of vertical movement) can be achieved with Invisalign.
That said some types of vertical movements (and horizontal ones too) can be difficult with Invisalign. I wouldn't let New Beauty decide what type of treatment I need. See an orthodontist experienced with Invisalign and let them help you reach your goals for a great smile.